Question

If the level of glucose in the blood (milligrams per deciliter of blood) after 12-hour fast for people under 50 years old is normally distributed with a mean of 90 and standard deviation of 24. If a test was randomly picked what is the probability that the level of glucose is less than 30?

Answer 1

X ~ N ( µ = 90 , σ = 24 )
P ( X < 30 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 30 - 90 ) / 24
Z = -2.5
P ( ( X - µ ) / σ ) < ( 30 - 90 ) / 24 )
P ( X < 30 ) = P ( Z < -2.5 )
P ( X < 30 ) = 0.0062